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Axiom ax-addcl 9081
Description: Closure law for addition of complex numbers. Axiom 4 of 22 for real and complex numbers, justified by theorem axaddcl 9057. Proofs should normally use addcl 9103 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )

Detailed syntax breakdown of Axiom ax-addcl
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 9019 . . . 4  class  CC
31, 2wcel 1727 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1727 . . 3  wff  B  e.  CC
63, 5wa 360 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 9024 . . . 4  class  +
81, 4, 7co 6110 . . 3  class  ( A  +  B )
98, 2wcel 1727 . 2  wff  ( A  +  B )  e.  CC
106, 9wi 4 1  wff  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )
Colors of variables: wff set class
This axiom is referenced by:  addcl  9103
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